Question

Find the derivative of the following function, with a positive index (differentiation)

Answer 1

Answer:

2nd option

Step-by-step explanation:

Using the power rule

$\frac{d}{dx}$ (a$x^{n}$ ) = na$x^{n-1}$

Given

f(x) = $\frac{3}{2\sqrt[3]{x} }$ = $\frac{3}{2x^{\frac{1}{3} } }$ = $\frac{3}{2}$ $x^{-\frac{1}{3} }$ , then

f'(x) = - $\frac{1}{3}$ × $\frac{3}{2}$ $x^{-\frac{4}{3} }$

      = - $\frac{1}{2}$ × $\frac{1}{x^{\frac{4}{3} } }$

      = - $\frac{1}{2x^{\frac{4}{3} } }$ = - $\frac{1}{2\sqrt[3]{x^4} }$ [ Note there should be a leading negative ]